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LenKa [72]
4 years ago
12

A number t decreased by 2 is at least 7

Mathematics
1 answer:
9966 [12]4 years ago
6 0
Answer:
t - 2 ≥ 7; t ≥ 9

Explanation:
“a number t” = t
“decreased by 2” = - 2
“Is at least 7” = ≥ 7
So, t - 2 ≥ 7

To solve for t - 2 ≥ 7, add 2 to both sides of the equation

t - 2 ≥ 7
t - 2 + 2 ≥ 7 + 2
t ≥ 9

So, t ≥ 9
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In a study to find the proportion of children with asthma in a certain population, we desire a 95% confidence interval with stan
soldier1979 [14.2K]

Answer:

The minimum sample size should be of 381.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of \pi, and a confidence level of 1-\alpha, we have the following confidence interval of proportions.

\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}

In which

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The margin of error is given by:

M = z\sqrt{\frac{\pi(1-\pi)}{n}}

95% confidence level

So \alpha = 0.05, z is the value of Z that has a pvalue of 1 - \frac{0.05}{2} = 0.975, so Z = 1.96.

Without any prior knowledge of the proportion, what should be our minimum sample size

We dont know the population proportion, so we use \pi = 0.5, which is when the largest sample size is needed. We have to find n for which M = 0.05. So

M = z\sqrt{\frac{\pi(1-\pi)}{n}}

0.05 = 1.95\sqrt{\frac{0.5*0.5}{n}}

0.05\sqrt{n} = 1.95*0.5

\sqrt{n} = \frac{1.95*0.5}{0.05}

(\sqrt{n})^2 = (\frac{1.95*0.5}{0.05})^2

n = 380.25

Rounding up

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